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Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing

Quantum limited digital holography and the limits of spatial heterodyne detection (Conference Presentation)

Thomas G. Brown

Published Mar 9, 2020• 0 citations
Publisher

Abstract

We analyze, and test experimentally, a method of imaging at very low light levels using spatial interference between a strong local oscillator field and a weak beam. By using Fourier phase recovery techniques familiar in classical interferometry and by correcting the inhomogeneities in the reference field, we can represent the quadrature components of a given spatial mode in the complex plane. Further, by post selection filtering (convolution and sampling), the method can distinguish photons of different orbital angular momentum with a one-count standard deviation consistent with the quantum noise floor.

DOI
10.1117/12.2553471

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We analyze, and test experimentally, a method of imaging at very low light levels using spatial interference between a strong local oscillator field and a weak beam. By using Fourier phase recovery techniques familiar in classical interferometry and by correcting the inhomogeneities in the reference field, we can represent the quadrature components of a given spatial mode in the complex plane. Further, by post selection filtering (convolution and sampling), the method can distinguish photons of different orbital angular momentum with a one-count standard deviation consistent with the quantum noise floor.
We present a method of photon orbital angular momentum selection at very low light levels using spatial interference between a strong local oscillator field and a weak beam. By using Fourier phase recovery techniques familiar in classical interferometry, we can experimentally obtain a quantum-limited Q distribution with a standard deviation consistent with the quantum noise floor. Further, by projecting the complex Fourier peak on a Laguerre–Gauss basis, we can distinguish states of different orbital angular momentum with high fidelity for small numbers of counts per acquisition frame. The noise equivalent photoelectron count for this measurement is 10 − 5 counts per pixel per frame.
The orbital angular momentum (OAM) provides a unique way of adding a degree of freedom to the information content of a photon. We show a method to sort the OAM content of a collimated laser beam at very low light levels by using spatial interference between the OAM beam and a strong local oscillator field. The resulting interferogram is analyzed in the Fourier domain. By further numerically filtering, the OAM content of the beam can be distinguished with a one-count standard deviation consistent with the quantum noise floor.
Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.
Summary form only given. The spatial structure of a photon has proved to be indispensable resource allowing the experimental realization of free-space quantum cryptography or high dimensional entanglement. Although efficient methods for manipulating spatial characteristic of individual photons can be easily transferred from the field of classical optics, their spatial structure cannot be measured using the standard interferometric reference-based methods such as optical holography due to their completely undefined-global phase. Hence, the full recovery of a transverse photon wavefunction still remains a challenging task tackled so far exclusively using indirect methods such as the quantum tomography [1] and weak values measurements [2].Here we present and experimentally demonstrate a different approach based on spatially resolved detection of two-photon interference [3,4]. Although such measurements are usually perceived to be insensitive to the relative phase between two interfering photons we show that rarely considered local phase dependence can be still observed and utilized for direct recovery of a single photon quantum wavefunction. In particular we experimentally show that the complex transversal wavefunction of the unknown photon can be fully recovered from the 2D spatial coincidence pattern resulting from its two-photon interference with the reference photon [5].
Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1 Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.
Spiral holographic imaging in the Hong-Ou–Mandel interference scheme is introduced. Using spontaneous parametric down-conversion as a source of photon pairs, we analyze the joint orbital angular momentum spectrum of a reference photon and the photon encoding information of the object. The first-order interference of light beams in standard holographic imaging is replaced by the quantum interference of two-photon probability amplitudes. The difficulty in retrieving the amplitude and phase structure of an unknown photon is thereby avoided as classical interferometric techniques such as optical holography do not apply. Our results show that the full information of the object's transmission function can be recorded in the spiral hologram, which originates directly from the joint orbital angular momentum spectrum. This presents a lateral demonstration of compressive imaging and can potentially be used for remote sensing.